Conservative North Somerset MP Liam Fox told the BBC it would be "unthinkable" if the health service was not among top priorities for spending after Brexit.
The international trade secretary, a former GP, told BBC Radio 4's Today programme there would be a "dividend from leaving the European Union" - to be spent on "the priorities we face at the time".
"I find it absolutely unthinkable that health would not be amongst the top of those," he said.
His fellow Brexiteer, Foreign Secretary Boris Johnson, was rebuked on Tuesday for publicly calling for more money for the NHS ahead of a confidential Cabinet meeting.
The Liberal Democrat Lords spokesman on Europe, Baroness Ludford, questioned whether there would be any extra money to spend, tweeting: "Far from a dividend, Brexit means lower growth & thus public spending."